Mulligans, part 2

by MTGViolet

Now, finally, for some practical application!

We spent the last several weeks learning how to calculate things like how likely a given mix of cards in your hand is and developing a metric to decide how long we have to wait until we draw a given number of lands and so on. Now to put that all into play.

The nice thing about this sort of math is, you can figure it out all in advance. In fact, I’m thinking of, after my move (I’m moving, by the way), writing a small app that will let you type in the stats of your deck and then automatically make sort of a spreadsheet that helps you make mulliganing decision.

The crux of the matter is, as you might have already suspected, comparing the expected time to draw a given number of lands (we’ll say four, for the sale of argument) based on the cards you already have in hand to the more vague number you would get if you throw your cards back and draw six more. If the number for the six-card-hand is lower, you mulligan. If it’s higher, you throw it back.

Which works wonderfully… Until you sit on a seven-land opening hand and are pleased as punch that the number can’t get any lower.

…okay, not really. We can’t just look at the number of lands, we have to look at the number of non-lands as well. So, we’ll perform the same calculations, but with non-lands instead of lands. Just switch out the numbers, and compare them again. This can all be done beforehand and easily memorized before you sit at the table. You might even want to modify these a bit. Say, you want to include other mana sources in with the lands, that’s fine. Say there are some non-land cards you’d per not to have in your opening hand, just subtract them from the second set. At the end of the day, your gut is going to play into this a lot, however once you have the charts, and the flowchart of mulliganing decisions, you can do yourself one big favor.

Stick to them. Don’t go by your gut, stay with the raw numbers. Why do this, do you ask? Is is analysis so bulletproof that you can’t do any better? Well, no, not by a long shot, but what I’ve seen time after time, and I’m even guilty of this myself, is players will second guess themselves. I’ll go, “oh, well, I only have one land, but two of my spells cost two, so I just need one more to go off…” and the use myself for being mana screwed for the whole game. No, once you get used to playing by the quote unquote rules, then you can start modifying it for those corner cases where the rules may say one thing, but the cards themselves give you slightly better odds.

Of course, this only covers mono-colored decks. When dealing wi multiple colors, things get a bit mo complex, but not really more complicated. The same principles apply, just evaluating them takes a bit more work. Again, a simple program could figure these out and even help you with your deck building. But that, as they say, is a topic for another day.

Exercises

  • Take your favorite deck and draw up a mulligan choice flowchart for it
  • Write the author of your favorite math-related magic blog and bug him about writing the app he mentioned.
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